Theorem fneq1i 5414

Description: Equality inference for function predicate with domain. (Contributed by Paul Chapman, 22-Jun-2011.)

Hypothesis

Ref	Expression
fneq1i.1	|- F = G

Assertion

Ref	Expression
fneq1i	|- ( F Fn A <-> G Fn A )

Proof of Theorem fneq1i

Step	Hyp	Ref	Expression
1		fneq1i.1	. 2 |- F = G
2		fneq1 5408	. 2 |- ( F = G -> ( F Fn A <-> G Fn A ) )
3	1, 2	ax-mp 5	1 |- ( F Fn A <-> G Fn A )

Syntax hints:   <-> wb 105   = wceq 1395   Fn wfn 5312

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-3an 1004  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-sn 3672  df-pr 3673  df-op 3675  df-br 4083  df-opab 4145  df-rel 4725  df-cnv 4726  df-co 4727  df-dm 4728  df-fun 5319  df-fn 5320

This theorem is referenced by:  fnunsn  5429  fnopabg  5446  f1oun  5591  f1oi  5610  f1osn  5612  ovid  6120  tfri1d  6479  frec2uzrand  10622  frec2uzf1od  10623  frecfzennn  10643  xnn0nnen  10654  prdsinvlem  13636  dfrelog  15528  edgstruct  15858  nninfsellemeqinf  16341